Question

the graph of $y = |x|$ is shifted down by 9 units. what is the equation of the new graph? choose 1 answer: a $y = |x + 9|$ b $y = |x| + 9$ c $y = |x| - 9$ d $y = |x - 9|$

Explanation:

Step1: Recall vertical shift rule

For a function \( y = f(x) \), shifting down by \( k \) units (where \( k>0 \)) gives \( y = f(x)-k \).
Here, \( f(x)=|x| \) and \( k = 9 \).

Step2: Apply the rule

Substitute \( f(x)=|x| \) and \( k = 9 \) into the shift formula. So the new function is \( y=|x|-9 \).

Answer:

C. \( y = |x| - 9 \)